Robert,
Welcome to the forum. You've found a great bunch of folks!
In regards to your question, Bog has really stating it best. The size of equipment, shop space, the amount you want to or can spend, and the projects you want to tackle will dictate which way you will wind up going. You're post states you want to do small stuff, so I'll aim there.
For the following, I am going to make a couple of assumptions. Those being having a limited budget, and minimal experience in machining. If this isn't the case, please forgive me.
As Bog has said, and engine can be built with hand tools, so that would be the low end of the "small" spectrum, and will allow you to turn out some basic models. There is nothing wrong with that, and it can be a very rewarding way of building things. Some of the examples of engines built with basic hand tools are simply amazing.
For adding machinery, in my opinion, a small lathe would be the first thing that I would personally start shopping for. The prices range depending on size, options, brand, and country of manufacture. With that and some basic tooling, a lot can be done.
Going to the other side of the spectrum, you can buy a CNC lathe with all of the tooling and perform some complex work. As with anything in life, as the number of features increase, so does the price tag and complexity of use. As Bog has said, the sky is the limit as far as how much money can be sunk into the hobby! But, it doesn't have to be!
So, my advice would be to look at the types of projects you invision yourself doing, then set that as your aiming point. Define the equipment you would need for those projects. This doesn't mean that you can't buy a less capable machine, or smaller machine and then upgrade at a later time. Guys do this kind of thing to make sure that they will enjoy the hobby, have the skill, patience, or what ever reason. In saying this, if your target size lathe is a 12x24 for instance, but can only afford a 7x12, then take a look at how much you would not be able to do with the smaller machine. Odds are, the smaller machine will take you to a point in time that you can go for the bigger one, but in the interim time you are making chips.
Start shopping around and doing research on the different equipment you are in the market for to compare prices, capabilities, and the like. A side note, Grizzly has their product manuals online as do some of the others, and this can help you in answering some of the questions that are sure to arrise in capabilities, what something is for, etc. If you want or need to go a less expensive route, then shop around your area for used equipment. This method has some inherint risks associated with it (i.e. Do your homework before buying), but a bundle of money can be potentially saved if you find the "right" deal. There are bargins out there, but you have to be patient and persistent in your pursuits.
Until you have the tools/machinery/materials to tackle your first model, start reading through the different topics on this site and getting a feel for techniques used to perform the different tasks. A simple task can be made very difficult by doing more than needed to get the result that is desired. The many ways to do the same operation, so the operator has to interpret the best way for his/her skill level, experience, and capability.
And ask questions! If there is anything you are wondering about, or if something you see doesn't make sense, post it and the members here will help you out. Taking this one step futher, if you see a picture of a part, and can't figure out how it was machined, why it was set up in that way, what it is made out of, or whatever, then ask the question and have it explained to you. These guys really are willing to pass along the methods that work for them. We all learn from each other.
The most important thing is to have fun! This is a great hobby, and we are glad to have you on board!
